Comparative Analysis of the Efficiency of Sampling Scheme Estimators in Estimating Population Total

Sampling is a fundamental tool in statistical research, providing a practical alternative to complete enumeration where of time, cost, personal and accessibility are constraints Choosing the best estimator for population total estimation is one of the main issues in survey sampling. Even though many different sampling strategies and estimators are available, it is still difficult to assess how effective they are in diverse situations. This study presents a comparative analysis of the efficiency of sampling scheme estimators (Hansen Hurwitz, Horvitz-Thompson, Rao-Hartley-Cochran’s and Sen Yates-Grundy) in estimating population total using child birth data) from Ekiti State . Population totals and variances of each estimator were obtained and the most efficient estimator determined in terms of variance. The results revealed that the Rao–Hartley–Cochran estimator consistently produced the lowest population total estimates with the least variance for 2 years, while in the other year, the Sen–Yates–Grundy estimator demonstrated superior efficiency with minimal variance. (The study offers empirical evidence regarding the relative efficiency of the probability proportional to size estimators with replacement (Hansen–Hurwitz) and those without (Horvitz–Thompson, Rao–Hartley–Cochran, and Sen–Yates–Grundy in estimating population totals). The study further showed that' efficiency of estimators is not constant but rather fluctuates over time and across data distributions. The study also closes the gap between theoretical sampling principles and real-world application in demographic and health statistics by using these sample strategies on actual child birth registration data from Ekiti State.